The Kenyan Red Cross Society (KRCS) had earlier put the death toll at 69.

Two of the 10 to 15 militants holding hostages in the mall were shot dead in the fierce fighting to rescue the victims.

Meanwhile, Kenyan police said they have managed to rescue some of the hostages.

Inspector General of Police David Kimaiyo said security forces were trying to gain access from the rooftop of the Westgate shopping mall.

"Thumbs up to our multi-agency team, we have just managed to rescue some hostages. We are increasingly gaining advantage of the attackers," Kimaiyo said via his Twitter account.

"As we intensify our operations, we urge the public to stay away from Westgate and its environs for their own safety," he added, as ambulances were seen rushing to the mall.

Thick smoke was seen billowing Monday amid loud explosions at the mall on the third day of the tense standoff between security forces and Al-Shabaab militants.

Explosions were heard from inside the mall where hostages are believed to be held by their captors.

The insurgents from Somalia have claimed responsibility for the attack, saying it was revenge for a cross-border incursion by Kenyan soldiers into southern Somalia in October 2011.

So far, apart from two Indians confirmed dead, two French nationals, two Canadians, three Britons, one Chinese and one Ghanaian are among those who lost their lives in the attack.

In New Delhi, officials named two of the Indians killed as Sridhar Natarajan, 40, from Tamil Nadu and an employee of a local pharmaceutical firm Harley's Limited, and Paramshu Jain, eight, the son of Manoj Jain, the branch manager of Industrial Area Branch, Bank of Baroda (Kenya Limited).

Natarajan's wife Manjula Sridhar was injured in the attack. The mother and sister of Paramshu - Mukta Jain, 38, and Poorvi Jain, 12 - were also wounded.

The fourth injured is Natarajan Ramachandran, an employee of Flamingo Duty Free, Nairobi, according to official sources.

According to a report in the guardian.com, another Indian was shot when he failed to answer a question on Islam posed by a heavily armed gunman.

Joshua Hakim, who was in the mall, said that the gunmen spoke in Swahili for Muslims to identify themselves and leave.

Hakim covered the Christian name on his ID with his thumb and approached one of the attackers. He showed the plastic card.

"They told me to go. Then an Indian man came forward and they said, 'What is the name of Muhammad's mother?' When he couldn't answer they just shot him," he said.

It was not clear from the media report whether the Indian was injured or fatally shot.